Complete Lattice: Sieve (category theory)

Complete Lattice: Sieve (category theory)

If we define SieveC(c) (or Sieve(c) for short) to be the set of all sieves on c, then Sieve(c) becomes partially ordered under ⊆. It is easy to see from the definition that the union or intersection of any family of sieves on c is a sieve on c, so Sieve(c) is a complete lattice.

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